This book resulted from lectures given at the University of Erlangen–
Nuremberg and at the University of Magdeburg. On these occasions we
often had to deal with the problem of a heterogeneous audience composed
of students of mathematics and of different natural or engineering sciences.
Thus the expectations of the students concerning the mathematical accuracy
and the applicability of the results were widely spread. On the other
hand, neither relevant models of partial differential equations nor some
knowledge of the (modern) theory of partial differential equations could be
assumed among the whole audience. Consequently, in order to overcome the
given situation, we have chosen a selection of models and methods relevant
for applications (which might be extended) and attempted to illuminate the
whole spectrum, extending from the theory to the implementation, without
assuming advanced mathematical background. Most of the theoretical
obstacles, difficult for nonmathematicians, will be treated in an “inductive”
manner. In general, we use an explanatory style without (hopefully)
compromising the mathematical accuracy.
We hope to supply especially students of mathematics with the information
necessary for the comprehension and implementation of finite
element/finite volume methods. For students of the various natural or
engineering sciences the text offers, beyond the possibly already existing
knowledge concerning the application of the methods in special fields, an
introduction into the mathematical foundations, which should facilitate the
transformation of specific knowledge to other fields of applications.